Question 5 [20 marks] A bank wanted to find out whether the number of loan applications received is influenced by the current loan interest rate.

The manager selected 11 monthly periods for which different interest rates applied and recorded the number of loan applications received. Loan application received Interest rate (%) Loan applications 7 18 4.5 22 5.5 30 6 24 8 16 8.5 18 6 28 6.5 27 7.5 20 8 17 6 21

(a) Identify the independent variable and the dependent variable. [2]

(b) Show the data graphically in a scatter plot. What relationship is observed? [3]

(c) Calculate the Pearson's correlation coefficient between the rate of interest and the number of loan applications received. Comment on the strength of the association. [6]

(d) Derive the least squares regression line between the rate of interest and the number of loan applications received. [7]

(e) Interpret the meaning of the regression coefficient of the independent variable. [2]